Statistics for Iwasawa invariants of elliptic curves, $\rm{III}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929313362739200 |
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| author | Ray, Anwesh |
| author_facet | Ray, Anwesh |
| contents | Given a prime $p\geq 5$, a conjecture of Greenberg predicts that the $μ$-invariant of the $p$-primary Selmer group should vanish for most elliptic curves with good ordinary reduction at $p$. In support of this conjecture, I show that the $5$-primary Iwasawa $μ$- and $λ$-invariants simultaneously vanish for an explicit positive density of elliptic curves $E_{/\mathbb{Q}}$. The elliptic curves in question have good ordinary reduction at $5$, and are ordered by their height. The results are proven by leveraging work of Bhargava and Shankar on the distribution of $5$-Selmer groups of elliptic curves defined over $\mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Statistics for Iwasawa invariants of elliptic curves, $\rm{III}$ Ray, Anwesh Number Theory 11R23, 11R45, 11G05 Given a prime $p\geq 5$, a conjecture of Greenberg predicts that the $μ$-invariant of the $p$-primary Selmer group should vanish for most elliptic curves with good ordinary reduction at $p$. In support of this conjecture, I show that the $5$-primary Iwasawa $μ$- and $λ$-invariants simultaneously vanish for an explicit positive density of elliptic curves $E_{/\mathbb{Q}}$. The elliptic curves in question have good ordinary reduction at $5$, and are ordered by their height. The results are proven by leveraging work of Bhargava and Shankar on the distribution of $5$-Selmer groups of elliptic curves defined over $\mathbb{Q}$. |
| title | Statistics for Iwasawa invariants of elliptic curves, $\rm{III}$ |
| topic | Number Theory 11R23, 11R45, 11G05 |
| url | https://arxiv.org/abs/2404.09009 |